OPTIMALITY AND DUALITY IN NONSMOOTH VECTOR OPTIMIZATION INVOLVING GENERALIZED INVEX FUNCTIONS

  • Kim, Moon-Hee (Department of Multimedia Engineering, Tongmyong University)
  • Received : 2010.04.23
  • Accepted : 2010.06.23
  • Published : 2010.09.30

Abstract

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

Keywords

References

  1. F. H. Clarke, Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication, John Wiley & Sons, 1983.
  2. M. A. Hanson, On sufficienty of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80(1981), 545-550. https://doi.org/10.1016/0022-247X(81)90123-2
  3. M. H. Kim, Duality theorem and vector saddle point theorem for nonsmooth vector optimization problem, J. Appl. Math. & Computing 18(2005), 539-551.
  4. G. M. Lee, D. S. Kim and P. H. Sach, Characterization of Hartley proper efficiency in nonconvex programs, J. Global. Optim. 33(2005), 273-298. https://doi.org/10.1007/s10898-004-1935-0
  5. Y. Sawaragi, H. Nakayama and T. Tanino, Theory of Multiobjective Optimization, Academic Press, New York, 1985.
  6. P. H. Sach, G. M. Lee and D. S. Kim, Invex functions, nonsmooth alternative theorems and vector optimization problems, J. Global. Optim. 27(2003), 51-81. https://doi.org/10.1023/A:1024698418606